For quadratic programming (QP), it is usually assumed that the solving process is free of measurement noises or that the denoising has been conducted before the computation. However, time is precious for time-varying QP (TVQP) in practice. Preprocessing for denoising may consume extra time, and consequently violates real-time requirements. Therefore, a model with inherent noise tolerance is urgently needed to solve TVQP problems in real time. In this paper, we make progress along this direction by proposing a modified Zhang neural network (MZNN) model for the solution of TVQP. The original Zhang neural network model and the gradient neural network model are employed for comparisons with the MZNN model. In addition, theoretical analyses show that, without measurement noise, the proposed MZNN model globally converges to the exact real-time solution of the TVQP problem in an exponential manner and that, in the presence of measurement noises, the proposed MZNN model has a satisfactory performance. Finally, two illustrative simulation examples as well as a physical experiment are provided and analyzed to substantiate the efficacy and superiority of the proposed MZNN model for TVQP problem solving.

This technical note proposes a noise-tolerant zeroing neural network (NTZNN) design formula, and shows how recurrent (and recursive) methods for solving time-varying problems can be designed from the viewpoint of control. The NTZNN design formula provides a control-theoretic framework to deal with the convergence, stability and robustness issues of continuous-time (and discrete-time) models. NTZNN models derived from the proposed design formula demonstrate their advantages when applied to solving time-varying zero-finding problems in the presence of noises.

Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this paper, we propose a novel recurrent neural network to simultaneously address the periodic input disturbance, joint angle constraint, and joint velocity constraint, and optimize a general quadratic performance index. The proposed recurrent neural network applies to both regulation and tracking tasks. Theoretical analysis shows that, with the proposed neural network, the end-effector tracking and regulation errors asymptotically converge to zero in the presence of both input disturbance and the two constraints. Simulation examples and comparisons with an existing controller are also presented to validate the effectiveness and superiority of the proposed controller.

As a type of recurrent neural networks (RNNs) modeled as dynamic systems, the gradient neural network (GNN) is recognized as an effective method for static matrix inversion with exponential convergence. However, when it comes to time-varying matrix inversion, most of the traditional GNNs can only track the corresponding time-varying solution with a residual error, and the performance becomes worse when there are noises. Currently, zeroing neural networks (ZNNs) take a dominant role in time-varying matrix inversion, but ZNN models are more complex than GNN models, require knowing the explicit formula of the time-derivative of the matrix, and intrinsically cannot avoid the inversion operation in its realization in digital computers. In this article, we propose a unified GNN model for handling both static matrix inversion and time-varying matrix inversion with finite-time convergence and a simpler structure. Our theoretical analysis shows that, under mild conditions, the proposed model bears finite-time convergence for time-varying matrix inversion, regardless of the existence of bounded noises. Simulation comparisons with existing GNN models and ZNN models dedicated to time-varying matrix inversion demonstrate the advantages of the proposed GNN model in terms of convergence speed and robustness to noises.

Redundancy resolution is of great importance in the control of manipulators. Among the existing results for handling this issue, the quadratic program approaches, which are capable of optimizing performance indices subject to physical constraints, are widely used. However, the existing quadratic program approaches require exactly knowing all the physical parameters of manipulators, the condition of which may not hold in some practical applications. This fact motivates us to consider the application of adaptive control techniques for simultaneous parameter identification and neural control. However, the inherent nonlinearity and nonsmoothness of the neural model prohibits direct applications of adaptive control to this model and there has been no existing result on adaptive control of robotic arms using projection neural network (PNN) approaches with parameter convergence. Different from conventional treatments in joint angle space, we investigate the problem from the joint speed space and decouple the nonlinear part of the Jacobian matrix from the structural parameters that need to be learnt. Based on the new representation, we establish the first adaptive PNN with online learning for the redundancy resolution of manipulators with unknown physical parameters, which tackles the dilemmas in existing methods. The proposed method is capable of simultaneously optimizing performance indices subject to physical constraints and handling parameter uncertainty. Theoretical results are presented to guarantee the performance of the proposed neural network. Besides, simulations based on a PUMA 560 manipulator with unknown physical parameters together with the comparison with an existing PNN substantiate the efficacy and superiority of the proposed neural network, and verify the theoretical results.

Distributed consensus has been intensively studied in recent years as a means to mitigate state differences among dynamic nodes on a graph. It has been successfully employed in various applications, e.g., formation control of multirobots, load balancing, and clock synchronization. However, almost all the existing applications cast an impression of consensus as a simple process to iteratively reach agreement, without any clue on possibility to generate advanced complexity, say shortest path planning, which has been proved to be NP-hard. Counterintuitively, we show for the first time that the complexity of shortest path planning can emerge from a perturbed version of a min-consensus protocol, which as a case study may shed lights to researchers in the field of distributed control to rethink the nature of complexity and the distance between control and intelligence. Besides, we rigorously prove the convergence of graph dynamics and its equivalence to shortest path solutions. An illustrative simulation on a small-scale graph is provided to show the convergence of the biased min-consensus dynamics to shortest path solution over the graph. To demonstrate the scalability to large-scale problems, a graph with 43 826 nodes, which corresponds to a map of a maze in 2-D, is considered in the simulation study. Apart from possible applications in robot path planning, the result is further extended to robot complete coverage, showing its potential in real practice such as cleaning robots.